What is the solution for (1+ln(x)+y/x)dx+(-1+ln(x))dy=0 ?

The solution for (1+ln(x)+y/x)dx+(-1+ln(x))dy=0 is y=-(xln(x))/(-1+ln(x))+(c_{1})/(-1+ln(x))

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(1+ln(x)+y/x)dx+(-1+ln(x))dy=0

(1 + ln (x) + \frac{y}{x}) d x + (- 1 + ln (x)) d y = 0

y = - \frac{x ln ( x )}{- 1 + ln ( x )} + \frac{c _{1}}{- 1 + ln ( x )}

Solution steps

(1 + ln (x) + \frac{y}{x}) d x + (- 1 + ln (x)) d y = 0

Solve linear ODE:

y = - \frac{x ln ( x )}{- 1 + ln ( x )} + \frac{c _{1}}{- 1 + ln ( x )}

y = - \frac{x ln ( x )}{- 1 + ln ( x )} + \frac{c _{1}}{- 1 + ln ( x )}

y = e^{3 x} + 10 e^{2 x}

x \to 0 lim (\frac{2 e ^{x} - 2}{3 x})

t e^{\frac{- t}{2}}

\int \frac{1}{x ( x ^{2} - 81 ) ^{\frac{3}{2}}} d x

y = \frac{( x + 2 )}{( x + 1 ) ^{2}}, at x = 0

What is the solution for (1+ln(x)+y/x)dx+(-1+ln(x))dy=0 ?
The solution for (1+ln(x)+y/x)dx+(-1+ln(x))dy=0 is y=-(xln(x))/(-1+ln(x))+(c_{1})/(-1+ln(x))